Прогнозирование заказов такси¶
Цели исследования:
По историческим данным о заказах такси в аэропортах построить для заказчика «Чётенькое такси» модель предсказания количества заказов на следующий час с целью привлечения водителей в пиковые часы нагрузок.
Заказчику важно значение метрики RMSE на тестовой выборке, не превышающее 48 заказов.
Ход исследования:
- Подготовка данных
- Загрузка и знакомство с данными
- Анализ данных
- Обучение моделей для предсказания количества заказов
- Проверка выбранной модели на тестовых данных
- Итоговый вывод
Данные лежат в файле taxi.csv. Количество заказов находится в столбце num_orders (от англ. number of orders, «число заказов»).
Результаты исследования:
- Для достижения целей данные были ресемплированы до частоты в 1 час
- Временной ряд нестационарен, поэтому для его анализа применена техника декомпозиции, которая позволила выявить признаки, помогающие моделям эффективнее обучаться
- Методом кросс-валидации были обучены 4 регрессионные модели (Линейная регрессия, Случайный лес, LightGBM, CatBoost)
- Проведено тестирование лучшей модели по метрике RMSE, полученый результаты, удовлетворяющие критерию (
важно значение метрики RMSE на тестовой выборке, не превышающее 48 заказов) - Заказчику рекомендавана полученная модель
Подготовка данных¶
Загрузка библиотек¶
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from sklearn.model_selection import GridSearchCV, RandomizedSearchCV, train_test_split, TimeSeriesSplit
from sklearn.metrics import mean_squared_error
from sklearn.preprocessing import StandardScaler, PolynomialFeatures
from sklearn.ensemble import RandomForestRegressor
from sklearn.linear_model import LinearRegression
from catboost import CatBoostRegressor
from lightgbm import LGBMRegressor, plot_importance
from statsmodels.tsa.seasonal import seasonal_decompose
Загрузка и знакомство с данными¶
taxi = pd.read_csv('/home/panther/Documents/Deep Learning/datasets/taxi.csv', parse_dates=[0], index_col=[0])
taxi.head()
| num_orders | |
|---|---|
| datetime | |
| 2018-03-01 00:00:00 | 9 |
| 2018-03-01 00:10:00 | 14 |
| 2018-03-01 00:20:00 | 28 |
| 2018-03-01 00:30:00 | 20 |
| 2018-03-01 00:40:00 | 32 |
taxi.isna().sum()
num_orders 0 dtype: int64
taxi.info()
<class 'pandas.core.frame.DataFrame'> DatetimeIndex: 26496 entries, 2018-03-01 00:00:00 to 2018-08-31 23:50:00 Data columns (total 1 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 num_orders 26496 non-null int64 dtypes: int64(1) memory usage: 414.0 KB
Проверяю упорядоченность временной шкалы:
taxi.index.is_monotonic_increasing
True
Ресемплирую данные, объединяя заказы за каждый час:
taxi = taxi.resample('1h').sum()
taxi.shape
(4416, 1)
Глобальные переменные:
figsize = (12, 6)
target_col = 'num_orders'
min_date = taxi.index.min()
max_date = taxi.index.max()
Границы временного ряда:
print(f'Левая граница: {min_date}')
print(f'Правая граница: {max_date}')
print(f'Длина ряда: {max_date - min_date}')
Левая граница: 2018-03-01 00:00:00 Правая граница: 2018-08-31 23:00:00 Длина ряда: 183 days 23:00:00
Общий вид временного ряда:
ax = taxi.plot(title='Общий график количества вызовов такси по времени', figsize=figsize)
taxi.rolling(50).mean().plot(ax=ax, color='red', linewidth=1);
ax.legend(['Количество заказов в день', 'Скользящая средняя от количества заказов']);
ax.set_xlabel('Дата');
Выводы, подготовка данных¶
- Данные загружены из файла taxi.csv в датафрейм taxi с индексацией по колонке даты.
- В файле 26496 строк с данными по количеству заказов такси в каждые 10 минут за период с 2018-03-01 по 2018-08-31
- Проведено ресемплирование данных с аггрегацией почасовых заказов, получилось 4416 строк
Анализ данных временного ряда¶
Распределение данных и стандартные статистики¶
taxi.describe()
| num_orders | |
|---|---|
| count | 4416.000000 |
| mean | 84.422781 |
| std | 45.023853 |
| min | 0.000000 |
| 25% | 54.000000 |
| 50% | 78.000000 |
| 75% | 107.000000 |
| max | 462.000000 |
ax = taxi[target_col].plot.hist(bins=50, figsize=figsize);
mean = taxi[target_col].mean(); mode = taxi[target_col].mode()[0]
ax.axvline(mean, color='black', ls='--')
ax.axvline(mode, color='blue', ls='--')
ax.text(mean+5, 200, f'$\mu\ =\ {mean:.2f}\ (среднее)$')
ax.text(mode-35, 100, f'$\mu_o\ =\ {mode:.2f}\ (мода)$', color='blue');
ax.set(title='Распределение количества заказов', xlabel='Заказы', ylabel='Частота');
Данные имеют одномодальное правоасимметричное распределение (мода меньше среднего) с длинным правым хвостом, что говорит о том, что в данных имеются пиковые значения, существенно превышающие среднее.
Временной ряд нестационарный: среднее значение количества заказов со временем растет, также растет и дисперсия (std):
Среднее количество заказов и стандартное отклонение в первой половине ряда:
taxi.iloc[:taxi.shape[0]//2].agg(['mean', 'std'])
| num_orders | |
|---|---|
| mean | 65.003170 |
| std | 32.899422 |
Среднее количество заказов и стандартное отклонение во второй половине ряда:
taxi.iloc[taxi.shape[0]//2:].agg(['mean', 'std'])
| num_orders | |
|---|---|
| mean | 103.842391 |
| std | 47.098376 |
Иллюстрация нестационарности:
ax = taxi.resample('1d').sum().plot(figsize=figsize)
taxi.resample('1d').sum().rolling(10).mean().plot(ax=ax, color='red')
ax.set(title='Дневной график заказов такси', xlabel='Дата', ylabel='Количество')
ax.legend(['Количество заказов в день', 'Скользящая средняя от количества заказов']);
Анализ сезонной декомпозиции ряда¶
Функция постройки графика декомпозиции ряда:
def decompose(data, period_days, plot=['Тренд', 'Сезонность', 'Остатки'], returning=False, mov_avg=0):
# определение частотности ряда в типе timedelta и перевод периода (в днях) в период частоты ряда
delta = data.iloc[:2].apply(lambda x: x.index[1] - x.index[0])[target_col]
decomposed = seasonal_decompose(data, period=pd.to_timedelta(f'{period_days}d') // delta)
dec = {'Тренд': decomposed.trend, 'Сезонность': decomposed.seasonal, 'Остатки': decomposed.resid}
plt.figure(figsize=(figsize[0], figsize[1]*len(plot)))
plt.subplots_adjust(hspace=0.3)
for i, n in enumerate(plot): # в цикле динамически расширяется фигура для размещения графиков
ax = plt.subplot(len(plot), 1, i+1)
name = f' {n} (период окна декомпозиции: {period_days} дней)'
dec[n].plot(title=name, ax=ax, xlabel='Дата', ylabel='Количество заказов')
# если нужен график скользящей средней периода mov_avg
if mov_avg > 0:
dec[n].rolling(mov_avg).mean().plot(title=name, ax=ax, xlabel='Дата', ylabel='Количество заказов',
color='red')
# если нужно вернуть значения декомпозиции
if returning:
return dec['Тренд'], dec['Сезонность'], dec['Остатки']
Оценка трендовой компоненты ряда¶
decompose(taxi, period_days=30, plot=['Тренд'])
Тренд явно различим. От 60 вызовов в начале ряда количество вызовов растет до 130.
decompose(taxi, period_days=10, plot=['Тренд'])
В начале каждого месяца (кроме июля) наблюдаются провалы в количестве заказов.
При обучении модели для характеризации тренда могут пригодиться такой признак, как день года (dt.dayofyear).
Месячная сезонность¶
Пересемплирую данные из часов в дни, чтобы сезонность была различима:
decompose(taxi.resample('1d').sum(), period_days=30, plot=['Сезонность'], mov_avg=5)
Начало каждого месяца сопровождается падением относительно линии тренда, после чего идет рост до последней недели месяца, затем падение ниже линии тренда, заканчиающееся в начале следующего месяца.
Недельная сезонность¶
Данные за первые 2 недели:
decompose(taxi[min_date:min_date+pd.to_timedelta(30, unit='d')], 7, plot=['Сезонность'], mov_avg=5)
taxi.loc['2018-03-05'].index.day_name()[0]
'Monday'
Последние 2 недели:
decompose(taxi[max_date-pd.to_timedelta(14, unit='d'):max_date], 7, plot=['Сезонность'], mov_avg=5)
taxi.loc['2018-08-20'].index.day_name()[0]
'Monday'
Недельное пиковое значение количества вызовов приходится на понедельник. Видна зависимость высоты внутридневных пиков от дня недели. Для моделей понадобится признак дня недели: (dt.dayofweek)
Дневная сезонность¶
Первые 2 дня:
decompose(taxi[min_date:min_date+pd.to_timedelta(2, unit='d')], 1, plot=['Сезонность'])
Последние 2 дня:
decompose(taxi[max_date-pd.to_timedelta(2, unit='d'):max_date], 1, plot=['Сезонность'])
Меньше всего заказов приходится на утренние часы около 6:00, больше всего - на вечерние часы. Для обучения моделей понадобится признак часа (dt.hour)
Выводы, анализ данных временного ряда¶
- Исследуемый временной ряд не является стационарным
- При декомпозиции ряда, используя различные временные периоды, выявлена внутримесячная, внутринедельная и внутридневная сезонности
- На основе выявленных характеристик временного ряда предложены новые признаки:
- харатеризуюище тренд: день в году (
dt.dayofyear) - харктеризующие сезонность временного ряда: день недели (
dt.dayofweek), час (dt.hour)
- харатеризуюище тренд: день в году (
Обучение моделей¶
Уменьшаю размер датафрейма:
taxi[target_col] = pd.to_numeric(taxi[target_col], downcast='integer')
taxi.info()
<class 'pandas.core.frame.DataFrame'> DatetimeIndex: 4416 entries, 2018-03-01 00:00:00 to 2018-08-31 23:00:00 Freq: H Data columns (total 1 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 num_orders 4416 non-null int16 dtypes: int16(1) memory usage: 172.2 KB
Функции для обучения моделей и формирования признаков:
def make_features(data, max_lag, rolling_mean_size):
'''Функция генерации новых признаков временного ряда'''
data.loc[:, 'day_of_year'] = data.index.dayofyear.to_numpy().astype('int16')
data.loc[:, 'day_of_week'] = data.index.dayofweek.to_numpy().astype('int8')
data.loc[:, 'hour'] = data.index.hour.to_numpy().astype('int8')
for lag in range(1, max_lag+1):
data[f'lag_{lag}'] = data[target_col].shift(lag).interpolate().bfill().astype('int16')
data['rolling_mean'] = data[target_col].shift().rolling(rolling_mean_size).mean().interpolate().bfill().astype('float32')
def finetune(model_name, parameters, features, target, verbose=3, jobs=-1, **kwargs):
'''Фукнция подбора гиперпараметров
На вход принимает класс модели, решетку гиперпараметров для поиска, признаки и целевой признак
Возвращает лучшую из натренерованных моделей, её гиперпараметры и её луший результат по метрике RMSE
'''
cv = GridSearchCV(model_name(**kwargs), param_grid=parameters, scoring='neg_mean_squared_error',
cv=TimeSeriesSplit(n_splits=5), verbose=verbose, n_jobs=jobs)
cv.fit(features, target)
return cv.best_estimator_, cv.best_params_, np.sqrt(-cv.best_score_)
def print_cv_results(params, rmse):
'''Выводит результаты кросс-валидации на экран'''
print()
print(f'Лучшие параметры модели: {params}')
print(f'(train, CV) лучшее RMSE: {rmse:.2f}')
print()
Генерирую признаки (параметры задержки и периода сглаживания средней подобраны экспериментально):
params = {'learning_rate': [0.05449], 'max_bin': [40], 'num_leaves': [32]}
test_df = taxi.copy()
best_p = []
best_rmse = 9999
for lag in range(3, 30):
for avg in range(7, 40):
make_features(test_df, lag, avg)
t_features = test_df.drop([target_col], axis=1)
t_target = test_df[target_col]
t_features_train, t_features_test, t_target_train, t_target_test = train_test_split(
t_features, t_target, shuffle=False, test_size=0.1)
test_df = taxi.copy()
_, _, rmse = finetune(LGBMRegressor, params, t_features_train, t_target_train, verbose=0)
if rmse < best_rmse:
best_rmse = rmse
best_p.append((lag, avg, best_rmse))
print(best_p)
[(3, 7, 24.196688282311555), (3, 8, 24.0252403101438)]
make_features(taxi, 3, 8)
taxi
| num_orders | day_of_year | day_of_week | day | hour | lag_1 | lag_2 | lag_3 | rolling_mean | |
|---|---|---|---|---|---|---|---|---|---|
| datetime | |||||||||
| 2018-03-01 00:00:00 | 124 | 60 | 3 | 1 | 0 | 124 | 124 | 124 | 52.750 |
| 2018-03-01 01:00:00 | 85 | 60 | 3 | 1 | 1 | 124 | 124 | 124 | 52.750 |
| 2018-03-01 02:00:00 | 71 | 60 | 3 | 1 | 2 | 85 | 124 | 124 | 52.750 |
| 2018-03-01 03:00:00 | 66 | 60 | 3 | 1 | 3 | 71 | 85 | 124 | 52.750 |
| 2018-03-01 04:00:00 | 43 | 60 | 3 | 1 | 4 | 66 | 71 | 85 | 52.750 |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 2018-08-31 19:00:00 | 136 | 243 | 4 | 31 | 19 | 207 | 217 | 197 | 167.375 |
| 2018-08-31 20:00:00 | 154 | 243 | 4 | 31 | 20 | 136 | 207 | 217 | 163.500 |
| 2018-08-31 21:00:00 | 159 | 243 | 4 | 31 | 21 | 154 | 136 | 207 | 165.750 |
| 2018-08-31 22:00:00 | 223 | 243 | 4 | 31 | 22 | 159 | 154 | 136 | 164.875 |
| 2018-08-31 23:00:00 | 205 | 243 | 4 | 31 | 23 | 223 | 159 | 154 | 176.125 |
4416 rows × 9 columns
Разделение выборки на обучающую и тестовую (10% на тестовую):
features = taxi.drop([target_col], axis=1)
target = taxi[target_col]
features_train, features_test, target_train, target_test = train_test_split(features, target, shuffle=False,
test_size=0.1)
print(f'Размер тренировочной выборки: {features_train.shape}')
print(f'Размер тестовоый выборки: {features_test.shape}')
Размер тренировочной выборки: (3974, 7) Размер тестовоый выборки: (442, 7)
Линейная регрессия¶
%%time
params = {}
lr_best_model, lr_best_params, lr_best_rmse = finetune(LinearRegression, params, features_train, target_train)
print_cv_results(lr_best_params, lr_best_rmse)
Fitting 5 folds for each of 1 candidates, totalling 5 fits
Лучшие параметры модели: {}
(train, CV) лучшее RMSE: 31.74
CPU times: user 6.98 ms, sys: 7.81 ms, total: 14.8 ms
Wall time: 132 ms
Случайный лес¶
%%time
params = {'max_depth': [20, 21],
'n_estimators': [157, 158]}
rf_best_model, rf_best_params, rf_best_rmse = finetune(RandomForestRegressor, params,
features_train, target_train, random_state=42)
print_cv_results(rf_best_params, rf_best_rmse)
Fitting 5 folds for each of 4 candidates, totalling 20 fits
Лучшие параметры модели: {'max_depth': 21, 'n_estimators': 157}
(train, CV) лучшее RMSE: 24.27
CPU times: user 1.92 s, sys: 67.3 ms, total: 1.99 s
Wall time: 10.5 s
CatBoost¶
%%time
params = {
'learning_rate': [0.0279, 0.028, 0.0281],
'iterations': [1125, 1126, 1127],
'l2_leaf_reg': [2]
}
cb_best_model, cb_best_params, cb_best_rmse = finetune(CatBoostRegressor, params,
features_train, target_train, random_state=42)
print_cv_results(cb_best_params, cb_best_rmse)
Fitting 5 folds for each of 9 candidates, totalling 45 fits 1053: learn: 11.1544764 total: 3.39s remaining: 241ms 1054: learn: 11.1492351 total: 3.39s remaining: 238ms 1055: learn: 11.1450321 total: 3.4s remaining: 235ms 1056: learn: 11.1378002 total: 3.4s remaining: 231ms 1057: learn: 11.1327880 total: 3.4s remaining: 228ms 1058: learn: 11.1300024 total: 3.4s remaining: 225ms 1059: learn: 11.1232509 total: 3.4s remaining: 221ms 1060: learn: 11.1212207 total: 3.4s remaining: 218ms 1061: learn: 11.1153068 total: 3.41s remaining: 215ms 1062: learn: 11.1086966 total: 3.41s remaining: 212ms 1063: learn: 11.0997421 total: 3.41s remaining: 209ms 1064: learn: 11.0934746 total: 3.42s remaining: 205ms 1065: learn: 11.0893915 total: 3.42s remaining: 202ms 1066: learn: 11.0838958 total: 3.42s remaining: 199ms 1067: learn: 11.0785048 total: 3.42s remaining: 195ms 1068: learn: 11.0726518 total: 3.42s remaining: 192ms 1069: learn: 11.0695561 total: 3.42s remaining: 189ms 1070: learn: 11.0673645 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Лучшие параметры модели: {'iterations': 1127, 'l2_leaf_reg': 2, 'learning_rate': 0.028}
(train, CV) лучшее RMSE: 24.15
CPU times: user 3.6 s, sys: 400 ms, total: 4 s
Wall time: 54.3 s
LightGBM¶
%%time
params = {'learning_rate': [0.05449, 0.0545],
'num_leaves': [32, 33, 34],
'max_bin': [40]
}
lgbm_best_model, lgbm_best_params, lgbm_best_rmse = finetune(LGBMRegressor, params,
features_train, target_train, random_state=42)
print_cv_results(lgbm_best_params, lgbm_best_rmse)
Fitting 5 folds for each of 6 candidates, totalling 30 fits
Лучшие параметры модели: {'learning_rate': 0.0545, 'max_bin': 40, 'num_leaves': 33}
(train, CV) лучшее RMSE: 23.87
CPU times: user 267 ms, sys: 4.24 ms, total: 271 ms
Wall time: 618 ms
training_stats = pd.DataFrame({'Модель': ['Линейная регрессия', 'Случайный лес', 'CatBoost', 'LightGBM'],
'(train CV) RMSE': [round(x, 2) for x in [lr_best_rmse, rf_best_rmse, cb_best_rmse, lgbm_best_rmse]],
}).set_index('Модель').sort_values(by='(train CV) RMSE')
Выводы, обучение моделей¶
- На тренировочной выборке методом кросс-валидации были обучены модели Линейной регрессии, Случайного леса, CatBoost и LightGBM
- Получены следующие результаты:
training_stats
| (train CV) RMSE | |
|---|---|
| Модель | |
| LightGBM | 23.87 |
| CatBoost | 24.15 |
| Случайный лес | 24.27 |
| Линейная регрессия | 31.74 |
Заказчику рекомендуется использовать следующую модель:
best_model = training_stats.index[0]
best_model
'LightGBM'
Тестирование моделей¶
models = {'LightGBM': lgbm_best_model,
'CatBoost': cb_best_model,
'Линейная регрессия': lr_best_model,
'Случайный лес': rf_best_model}
pred_test = models[best_model].predict(features_test)
final_test_rmse = mean_squared_error(target_test, pred_test) ** 0.5
print(f'RMSE модели {best_model} на тестовых данных составил {final_test_rmse:.2f} заказов такси.')
RMSE модели LightGBM на тестовых данных составил 42.25 заказов такси.
График предсказаний для всей тестовой выборки:
plt.figure(figsize=figsize)
plt.plot(target_test.index, target_test, lw=0.8)
plt.plot(target_test.index, pd.Series(pred_test, index=target_test.index), color='green', lw=1);
plt.title('Тестовая выборка'); plt.xlabel('Дата'); plt.legend(['Фактические заказы', 'Предсказанные заказы']);
В большем масштабе:
plt.figure(figsize=(12, 6))
plt.plot(target_test['2018-08-25':'2018-08-29'].index, target_test['2018-08-25':'2018-08-29'], lw=0.8)
plt.plot(target_test['2018-08-25':'2018-08-29'].index,
pd.Series(pred_test, index=target_test.index)['2018-08-25':'2018-08-29'], color='green', lw=1);
plt.title('Тестовая выборка'); plt.xlabel('Дата'); plt.legend(['Фактические заказы', 'Предсказанные заказы']);
final_test_rmse < 48
True
Итоговый вывод¶
- С целью выявить лучшую модель для предсказания количества заказов на следующий час были обучены модели машинного обучения: Линейная регрессия, Случайный лес, Градиентный бустинг (CatBoost и LightGBM).
- В результате по критерию качества предсказания (
(train CV) RMSE); была сведена итоговая таблица с результатами обученных моделей:
training_stats
| (train CV) RMSE | |
|---|---|
| Модель | |
| LightGBM | 23.87 |
| CatBoost | 24.15 |
| Случайный лес | 24.27 |
| Линейная регрессия | 31.74 |
- Лучшей моделью по метрике RMSE оказалась:
best_model
'LightGBM'
- Тестирование модели показало следущие результаты:
print(f'RMSE модели {best_model} на тестовых данных составил {final_test_rmse:.2f} заказов такси.')
RMSE модели LightGBM на тестовых данных составил 42.25 заказов такси.
final_test_rmse < 48
True
- Можно заключить, что в рамках данного исследования удалось достичь показателя качества, установленного клиентом. Клиенту «Чётенькое такси» можно рекомендовать применение данной модели для целей прогнозирования на час количетва заказов такси по историческим данным.